Question 1 For each non-negative integer m, and each field K, let K[x] denote the vector space over K consisting of the polynomials in x with coefficients in K. Let K[z]m denote the subspace of K[x] consisting of the polynomials in 2 with coefficients in K and of degree

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Question 1
For each non-negative integer m, and each field K, let
K[x] denote the vector space over K consisting of the polynomials in x with coefficients
in K. Let K[z]m denote the subspace of K[x] consisting of the polynomials in 2 with
coefficients in K and of degree <m.
(b) Write down all e EQ such that the map f from Q[]2 to Q[2]4 given by
f(p(x)) = x²p(x)+cz is a linear map. Justify your answer.
Transcribed Image Text:Question 1 For each non-negative integer m, and each field K, let K[x] denote the vector space over K consisting of the polynomials in x with coefficients in K. Let K[z]m denote the subspace of K[x] consisting of the polynomials in 2 with coefficients in K and of degree <m. (b) Write down all e EQ such that the map f from Q[]2 to Q[2]4 given by f(p(x)) = x²p(x)+cz is a linear map. Justify your answer.
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